Whole numbers are like natural numbers. What differentiates them from natural numbers is that they start from 0 (zero), whereas natural numbers start from 1 (one). Whole numbers have the following four properties:

• Closure Property
• Associative Property
• Commutative Property
• Distributive Property

In this article, we will look at the distributive properties of whole numbers in-depth. 

Let us understand the meaning of the distributive property of whole numbers. The word “distribute” means dividing or sharing a part of something. As per the distributive property of numbers, multiplying the sum of two or more addends by a number gives the same result as multiplying each addend individually by the number and then adding the products together. We use the distributive property to break down complex and challenging problems into simple forms. In the distributive property of multiplication, we can break down a factor into a sum or a difference between two numbers.

The Distributive Property is an algebraic property required to multiply a single value and two or more values within a set of parenthesis. The distributive property refers to the operation performed on numbers available in brackets that can be distributed for each number outside the bracket. The distributive property is one of the most frequently used properties in Mathematics. Distributive property states that when a factor is multiplied by the sum/addition of two terms, it is essential to multiply each of the two numbers by the factor and perform the addition operation. It can be symbolically represented as:

X (Y+Z) = XY + XZ, where X, Y and Z are three different values.

Note: Though the division is the inverse of multiplication, the distributive law only holds in the case of division when the dividend is distributed or broken down. 

Distributive Property of Multiplication

The distributive property of multiplication can be expressed under both addition and subtraction. This means that the operation that exists inside the bracket, will be either addition or subtraction. 

Distributive Property of Multiplication Over Addition

The distributive property of multiplication is applicable over addition. The value is then multiplied by a sum. For example, say we have to multiply 4 with the result of the summation of 20 and 5. In this case, we can add the products and multiply 4 with the result of the sum in this manner:

4 * (20+5) = 4* 25 = 100.

We do not have to add up the sum if we apply the distributive property. So, we can find out the result at once in this manner:

4 (20) + 4 (5) = 80 + 20 = 100.

The result in both cases will be the same.

Distributive Property of Multiplication Over Subtraction

Distributive Property over Subtraction also works in a similar manner like Addition. Let us see an example in this case as well.

Suppose you are asked to subtract 6 from 10 and you are asked to multiply 6 with the result. How will you do it?

Mostly you will do it like, 6 *(10-6) = 6 *4 = 24

Using the Distributive Property, you can calculate the result in the below manner:

6*10 – 6*6 = 60 – 36 = 24

In this example, you can see that you were able to arrive at the same result through both the approaches. Understanding the concept of calculating the sums using distributive property proves useful. Also, it is good to be aware of both ways. Depending on the sum you get in the exam, you will be able to solve it in the manner that appears easier.

Distributive Property of Division

Now that you have learnt how to use the distributive property for additions and subtractions, here we will also learn how to use this property for the division of two numbers. The distributive property is not used as frequently for division as we use it for additions and subtractions. That said, if your concept about how to divide two numbers using distributive property is clear, you can use it to solve complicated problems, even in competitive exams. Let us understand how we can use the distributive property for divisions with the help of an example.

Suppose you have been asked to divide 120 by 6

Directly you can divide it like 120/6 = 20

Using the distributive property, you can solve it with the method of both addition and subtraction.

With addition,

We know 120 = 60 + 60 

Therefore 120/6 = (60+60)/6 = 60/6 + 60/6 = 10 + 10 = 20

With subtraction,

We know 120 = 180 – 60  

Therefore 120/6 = (180 – 60)/6 = 180/6 – 60/6 = 30 – 10 = 20

In all three methods, we get the same result.

We hope that this information on the distribution property of whole numbers has helped you. If you have any queries then you can visit our website.

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